The vessel was transporting sugar, and sank four nautical miles off Gabrik district in southern Hormozgan province, overlooking the Gulf of Oman, Mehrani added.
"The general condition of the crew is good", he said.
Bad weather has affected not only southern Iran but also Arab countries in the Gulf in recent days, with several issuing weather warnings.
The rainy weather system, expected to last until Friday in Iran, has caused flash flooding in the southern provinces such as Fars, Hormozgan, Kerman, and Sistan-Baluchistan (southeast).
The number of people killed because of the flooding has risen to nine, the head of Iran's Crisis Management Organization Esmail Najjar said.
Five people died in Fars province, and two in each of Kerman and Sistan-Baluchistan, Najjar told ISNA news agency on Wednesday.
Local rescue services had reported eight deaths on Tuesday.
The government will provide its "full capacity" to help people in affected areas, President Ebrahim Raisi pledged on Wednesday.
"It is necessary to fix the situation of the people immediately after the initial relief operation, so that they do not get into trouble," he was quoted as saying by state media.
At his instruction, a number of officials including vice-President Mohammad Mokhber and Energy Minister Ali Akbar Mehrabian, visited the flood-hit areas.
Mehrabian told a crisis management meeting in Sistan-Baluchistan that "there is a national determination to resolve the problems of the flood-hit areas", state TV said.
Largely arid, Iran has endured repeated droughts over the past decade, but also regular floods.
In 2019, heavy flooding in the country's south left at least 76 people dead and caused damage estimated at more than $2 billion.
Scientists say climate change amplifies droughts and that their intensity and frequency in turn threaten food security.